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| -rw-r--r-- | bezout.tex | 7 |
1 files changed, 4 insertions, 3 deletions
@@ -343,9 +343,10 @@ This is, to this order, precisely the Bézout bound, the maximum number of solutions that $N$ equations of degree $p-1$ may have \cite{Bezout_1779_Theorie}. That we saturate this bound is perhaps not surprising, since the coefficients of our polynomial equations -\eqref{eq:polynomial} are complex and have no symmetries. Analogous asymptotic -scaling has been found for the number of pure Higgs states in supersymmetric -quiver theories \cite{Manschot_2012_From}. +\eqref{eq:polynomial} are complex and have no symmetries. Reaching Bézout in +\eqref{eq:bezout} is not our main result, but it provides a good check. +Analogous asymptotic scaling has been found for the number of pure Higgs states +in supersymmetric quiver theories \cite{Manschot_2012_From}. More insight is gained by looking at the count as a function of $a$, defined by $\overline{\mathcal N}(\kappa,\epsilon,a)=e^{Nf(a)}$. In the large-$N$ limit, |